fine-tune
1. Literally, to make small and/or careful adjustments to a device, instrument, or machine. If you fine-tune your amp a little bit more, I think you'd get that tone you're looking for.
2. By extension, to make small and/or careful adjustments to an idea, plan, or strategy. I think if we fine-tuned our methodology, we'd have better success with this experiment.
fine-tune something
1. Lit. to make delicate adjustments in some mechanical or electronic device. It took a while to fine-tune the flute, but it was worth it.
2. Fig. to make small alterations in a plan or procedure. We need to spend some time fine-tuning the scheme, then we will seek approval.